Flexible cognition requires working memory (WM), the ability to form and manipulate mental representations. The contents of working memory include internally-generated factors required to determine which of many possible behavioral contingencies, or rules, should be applied under varying circumstances. Such an ability to flexibly invoke behavioral contingencies underlies many crucial functions, for example the cognitive regulation of emotion and context-dependent decision-making. In primates, the retention and manipulation of WM representations depends on the prefrontal cortex (PFC), and in humans, dysfunction of the PFC is associated with range of symptoms in psychiatric illness such as the neurocognitive deficits in schizophrenia. Neurons in PFC produce persistent spiking activity during behaviors that require WM, suggesting a mechanism by which mnemonic mental representations are maintained across time in the absence of a stimulus to drive activity. Although many PFC neurons respond most vigorously during WM of a specific stimulus feature to which they are specialized, a large proportion of PFC neurons actually exhibit mixed selectivity: heterogenous and time-varying responses to complex mixtures of remembered stimulus features. Nonlinear mixing is theorized to serve a pivotal role in flexible cognition by enabling high-dimensional representations from which simple linear readouts can extract many more task-related variables than if the neurons were highly specialized. How both the degree of nonlinearity and the dimensionality of representations are dynamically related to factors such as cognitive demand or learning remains larely unexplored. I propose to evaluate the proposition that nonlinear mixed-selectivity neurons give rise to distributed, high-dimensional representations suited to the higher cognitive functions for which they are invoked. This hypothesis asserts that substantial information exists in population-level structure which would be evident in the joint activity of a large number of neurons, and most apparent in an animal performing a cognitively demanding task for which successful completion necessitates formation of a high-dimensional representation. To test this assertion, I will use arrays of microelectrodes chronically implanted in the PFC of monkeys to record, in parallel, the activity of many single units while monkeys perform a delayed match to sample (DMS) task in which matches are based on conjunctions of features of the probe and sample stimuli. Because the matches are based on conjunctions, the decision rule can be made more or less complex and hence would require a representation of higher or lower dimension. I will examine how dimensionality of representations and the degree of nonlinear mixing is dynamically related to learning and task performance, and I will test the hypothesis that the complexity of the decision rule predicts the dimensionality of a neural representation during performance of the task. I will then examine whether or not the dimensionality of the representation is a constraint on successful performance of the task. Finally, I will investigate how the dimensionality of neural representations and the degree of nonlinear mixing evolves during learning of task rules.